Forum Problem Lists Definitions FAQ

11.37 (1990)

Partially Solved

a) Can the free Burnside group $B(m, n)$, for any $m$ and $n$, be given by defining relations of the form $v^n = 1$ such that for any natural divisor $d$ of $n$ distinct from $n$ the element $v^d$ is not trivial in $B(m, n)$?
b) Can the free Burnside group $B(m, n)$, for any $m$ and $n = 2^l \gg 1$, be given by defining relations of the form $v^n = 1$ such that for any natural divisor $d$ of $n$ distinct from $n$ the element $v^d$ is not trivial in $B(m, n)$?

Contributor: S. V. Ivanov

Progress

a) This is true for odd $n \geqslant 665$, and for all $n \geqslant 2^{48}$ divisible by $2^9$.
b) Yes, it can (S. V. Ivanov, Int. J. Algebra Comput., 4, no. 1–2 (1994), 1–308).

Comments

All comments are the responsibility of the user. Comments appearing on this page are not verified for correctness. Please keep posts mathematical and on topic. If you want to submit a proof (or a partial proof), please use the dedicated proof submission form rather than posting it in the comments.
Order by newest first or oldest first.

No comments yet. Be the first to comment.

Proof claims

Proof claims are the responsibility of the submitter. Appearance here does not mean the claim has been checked for mathematical correctness. Moderators only screen for spam, abuse, and obviously low-effort submissions.

No proof claims yet.